> So I readily read one in three households, as strictly more than one in three persons

That's a bad reading. Even if everyone in a household with a gun owner have access to guns, that would mean 33% of households implies exactly 33% of people if gun ownership is distributed among households with no bias by household size. It doesn't imply more than 33% of people unless gun owning households are larger than non-gun-owning households.

Why even care about this meaningless distinction? Households can give other households guns. What's important is if there are enough guns and ammunition for every person, not how they are distributed unless it's extremely skewed to a very specific part of the population.